1. Purpose
Understand how the total energy in a closed system is conserved during heat exchange.
Learn how to determine specific heat capacities of certain materials.

2. The Heat Capacity of an Object
Amount of heat (energy) that needs to be added to the object in order to raise its temperature by 1 degree Kelvin.
Heat added
(in Joules)
Change in Temperature
(in Kelvin)
Heat capacity
(in Joules/Kelvin)
If Q > 0 then Tfinal > Tinitial (temperature rises)
If Q < 0 then Tfinal < Tinitial (temperature drops)

3. The heat capacity depends on: Type of Material
Amount of the material (more water has more heat capacity……… you need more energy to raise its temperature………
The specific heat capacity is defined as
and has units of or
The specific heat capacity only depends on the material,
not on the amount of the material.

4. The Specific Heat Capacity
Amount of heat (energy) per unit mass that needs to be added to a material in order to raise its temperature by 1 degree Kelvin.
Heat added
(in Joules)
Change in Temperature
(in Kelvin)
Specific Heat capacity
mass of the object

5. Example and Implications of Specific Heat Capacity
A calorie is defined as the amount of heat that needs to be added to 1 gram of water in order to raise its temperature by 1 degree Kelvin.
Water has a relatively high heat capacity, which is important in biology and engineering:
Prevents your body (= mostly water) from heating up too quickly during exercise (an apple
that contains 60Kcal of energy has the potential to raise the temperature of a 60Kg
person by only
DT = Q/(c*m) = 60000cal/(1 cal g-1K –1 * 60000g)=1Kelvin
(assuming all the energy in the apple would go to heat and none to work performed)
Is a good coolant for engines (can absorb a lot of heat without having its temperature rise a lot.

6. Heat Transfer Between Two Objects (assume no heat is lost to the environment)
m c1
T1, initial
T2, initial
m c2
Before contact:
After reaching
thermal equilibrium
they both have the
same temperature
m c1
T2, final
m c2
T1, final
T1, final = T2, final = Tfinal
Given: m1, m2, c1, c2, T1,initial, T2,initial (Tfinal unkown)

7. Because no heat is lost to (or gained from) the environment:
The originally colder object gains energy (a positive Q)
The originally hotter object looses energy (a negative Q)
 Solve for Tfinal

8. Activity 1: Calibration of Temperature Probe
Alcohol thermometer (read off
temperature here)
Temp. Probe
750 Interface
Use ice bath and warm water bath for the two calibration points

9. Activity 2: Specific Heat Capacity / Power Output of Heater
Styrofoam cup filled with 150 ml water. Make sure heater doesn’t touch styrofoam !!!!!
Stand +
clamp
Red LED: Heater is ON
Computer:
Data Studio
Switches
Heater on/off
heater
Heater
Switch Box
Temp. Probe
750 Interface
Make sure this is plugged in the right way (ground to ground); ground is marked on tape

10. Activity 2: Specific Heat Capacity
Switch heater on and monitor the rise of the temperature
First run with heater
power connected.
Temperature DT
Second run with heater
power disconnected from
outlet.
time
Heater off
Heater on Dt
Note: The temperature may still rise after you turn the heater off (it gets turned off when you hit the “STOP” button in Data Studio).
Problem: Data Studio stops monitoring the temperature after “STOP” is hit.
Solution: After you hit the “STOP” button, unplug the main power (outlet) from the heater box. Then hit “START” again to monitor the temperature without further heating.

11. Activity 2: Specific Heat Capacity
Determine power output of the heating element.
Power = Energy / time = c m DT / Dt
This is the heat/energy
given off to the water
( = “Q” )
Compare your result to the power rating written
on the heating element.

12. Activity 3: Measure Specific Heat Capacity of Isopropyl Alcohol
Design an experiment to measure c isopropyl alcohol
Use your measured power rating of the heating element.
DO NOT DRAIN THE ISOPROPYL ALCOHOL INTO THE SINK !!!!! It is illegal to do that and we also do not want to waste the alcohol – it costs money.
Instead, please pour it back into the container from which you got it.

13. Activity 4: The Transfer of Heat
Caution: This experiment uses liquid nitrogen, which is extremely cold. Follow the safety instructions in your lab manual!!!!
Step 2:
Put cold brass (-197ºC)
into water.
Step 1:
Cool brass in the LN2
(wait until bubbling stops)
Step 3:
Monitor
temperature
Brass disc
on a string
Water at Room
Temperature
Liquid nitrogen (LN2)

14. Activity 4: The Transfer of Heat
Step 4: Determine the specific heat capacity of brass
Step 5: Compare your value of cbrass to that in the literature
(you can surely find that value on the internet)

15. Hints
Do not be surprised if the power rating of the heater element disagrees with what you measured. When we measured the resistance of the heating elements with wires, some were as high as 2 Ohms.
Therefore, a more realistic power rating may be about
…and it may be even lower if the supplied voltage is less than 12 Volts (on some of the heater boxes)  That’s why you need to use your measured power rating in Activity 3, not the official rating.